diff --git a/Tests/test_jp2k_leak.py b/Tests/test_jp2k_leak.py
new file mode 100644
index 000000000..ffd061e00
--- /dev/null
+++ b/Tests/test_jp2k_leak.py
@@ -0,0 +1,30 @@
+from helper import unittest, PillowTestCase, tearDownModule
+import sys
+
+from PIL import Image
+from resource import setrlimit, RLIMIT_AS, RLIMIT_STACK
+
+# Limits for testing the leak
+mem_limit = 512*1048576
+stack_size = 8*1048576
+iterations = (mem_limit/stack_size)*2
+codecs = dir(Image.core)
+test_file = "Tests/images/rgb_trns_ycbc.jp2"
+
+@unittest.skipIf(sys.platform.startswith('win32'), "requires Unix or MacOS")
+class TestJp2kLeak(PillowTestCase):
+    def setUp(self):
+        if "jpeg2k_encoder" not in codecs or "jpeg2k_decoder" not in codecs:
+            self.skipTest('JPEG 2000 support not available')
+
+    def test_leak(self):
+        setrlimit(RLIMIT_STACK, (stack_size, stack_size))
+        setrlimit(RLIMIT_AS, (mem_limit, mem_limit))
+        for count in range(iterations):
+            with Image.open(test_file) as im:
+                im.load()
+                im.close()
+
+
+if __name__ == '__main__':
+    unittest.main()